9783110550405 - periodic differential equations in the plane: a topological perspective: 29 di ortega, rafael (20 risultati)

Lingua: Inglese
Editore: De Gruyter, 2019
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Lingua: Inglese
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Lingua: Inglese
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Hardback. Condizione: New. Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of non…local results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré-Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.

Lingua: Inglese
Editore: De Gruyter, 2019
Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Lingua: Inglese
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Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introd…uction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to 'non-rigorous proofs'. In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré-Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.

Lingua: Inglese
Editore: De Gruyter, 2019
Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Condizione: New. 1st edition NO-PA16APR2015-KAP.

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Hardcover. Condizione: Brand New. 1st edition. 212 pages. 9.44x6.69x0.60 inches. In Stock.

Lingua: Inglese
Editore: De Gruyter, DE, 2019
Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Hardback. Condizione: New. Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of non…local results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré-Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.

Lingua: Inglese
Editore: De Gruyter, 2019
Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Condizione: New. 2019. Hardcover. . . . . .

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Lingua: Inglese
Editore: De Gruyter Mai 2019, 2019
Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermaniaBuchWeltWeit Ludwig Meier e.K.
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is bas…ed on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to 'non-rigorous proofs'. In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré-Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book. 200 pp. Englisch.

Lingua: Inglese
Editore: De Gruyter, 2019
Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Rafael Ortega, University of Granada, Spain.Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effe…cts. The most tra.

Lingua: Inglese
Editore: De Gruyter, De Gruyter Mai 2019, 2019
Serie: Libro 28 di 39 - De Gruyter Series in Nonlinear Analysis and Applications
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Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germaniabuchversandmimpf2000
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based o…n the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions.Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions.The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to 'non-rigorous proofs'. In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincaré¿Bendixson theorem for discrete dynamical systems.Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.Walter de Gruyter, Genthiner Straße 13, 10785 Berlin 200 pp. Englisch.